Measuring nonlocal Lagrangian peak bias

Abstract

We investigate nonlocal Lagrangian bias contributions involving gradients of the linear density field, for which we have predictions from the excursion set peak formalism. We begin by writing down a bias expansion which includes all the bias terms, including the nonlocal ones. Having checked that the model furnishes a reasonable fit to the halo mass function, we develop a 1-point cross-correlation technique to measure bias factors associated with 2-distributed quantities. We validate the method with numerical realizations of peaks of Gaussian random fields before we apply it to N-body simulations. We focus on the lowest (quadratic) order nonlocal contributions. We can reproduce our measurement of \chi_{10} if we allow for an offset between the Lagrangian halo center-of-mass and the peak position. The sign and magnitude of \chi_{10} is consistent with Lagrangian haloes sitting near linear density maxima. The resulting contribution to the halo bias can safely be ignored for M = 10^13 Msun/h, but could become relevant at larger halo masses. For the second nonlocal bias \chi_{01} however, we measure a much larger magnitude than predicted by our model. We speculate that some of this discrepancy might originate from nonlocal Lagrangian contributions induced by nonspherical collapse.